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Effective Action, Boundary Conditions, and Virasoro Algebra for AdS$_3$ · Around

2010

Effective Action, Boundary Conditions, and Virasoro Algebra for AdS$_3$

Porfyriadis, Achilleas P., Wilczek, Frank

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We construct, to second order, the effective action of General Relativity for small excitations generated by a vector field and use it to study conformal symmetry in the boundary of AdS$_3$.

By requiring finiteness of the boundary effective action(s) for certain asymptotic transformations, we derive the well-known Virasoro algebra and central charge associated with the boundary of AdS$_3$.
The bulk action for these transformations can be arbitrarily small.

Built on

R. M. Wald, General Relativity
1984
Earlier work this paper cites.
M. Henneaux and C. Teitelboim, “Asymptotically Anti-De Sitter Spaces,” Commun. Math. Phys. 98
1985
Earlier work this paper cites.
J. D. Brown and M. Henneaux, “Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,” Commun. Math. Phys. 104
1986
Earlier work this paper cites.

Similar

M. Banados, C. Teitelboim and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69
1992
Cited alongside, same era.
M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli, “Geometry of the (2+1) black hole,” Phys. Rev. D 48
1993
Cited alongside, same era.
A. Strominger, “Black hole entropy from near-horizon microstates,” JHEP 9802
1998
Cited alongside, same era.
A. Castro, A. Maloney and A. Strominger, “Hidden Conformal Symmetry of the Kerr Black Hole,” arXiv:1004.0996 [hep-th]
Original
Cited in the paper.

Then

J. M. Bardeen and G. T. Horowitz, “The extreme Kerr throat geometry: A vacuum analog of AdS(2) x S(2),” Phys. Rev. D 60
1999
Later among the works it cites.
M. Guica, T. Hartman, W. Song and A. Strominger, “The Kerr/CFT Correspondence,” Phys. Rev. D 80
Original
2009
Later among the works it cites.
I. Bredberg, T. Hartman, W. Song and A. Strominger, “Black Hole Superradiance From Kerr/CFT,” JHEP 1004
Original
2010
Closest in time.

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